How to Find the Focal Point of an Ellipse

Ellipses, also known as ovals, are used in almost every type of design. Jewelers, fashion designers, computer programmers, architects, logo makers and graphic designers all use ellipses to create designs that have appeal. Knowing how to find the focal points of an ellipse will help you design more appealing designs that are based on ellipses. Because the focal points of an ellipse are symmetrical about the center of the ellipse and mathematically related to the the ellipse itself, you can place design elements at the focal points to emphasize design symmetry -- a essential element of professionally designed works of art.

Things You'll Need

  • Oval template
  • Ruler
  • Graph paper
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Instructions

    • 1

      Draw a rectangle to be used as a bounding box for an ellipse. Draw the rectangle such that it has a height of 1 inch and length of 2 inches and that the length is parallel to the lower edge of your paper. Construct two diagonals within the rectangle that connect the opposing vertices of the rectangle. Label the point where the two diagonals intersects as "C" for the "center of the ellipse."

    • 2

      Draw a horizontal line through "C" that extends from the left edge of the rectangle to the right edge of the rectangle. Label this line as "MA" as an abbreviation for the "major axis" of the ellipse. Label the point where the major axis intersects the right side of the rectangle as "A."

    • 3

      Draw a vertical line through "C" that extends from the lower edge of the rectangle to the upper edge of the rectangle. Label this line as "MIA" as an abbreviation for the "minor axis" of the ellipse. Label the point where the minor axis intersects the top side of the rectangle as "B."

    • 4

      Inscribe an oval within the rectangle such that the oval's far left and far right points correspond to the points of intersection of the major axis and the rectangle and the oval's highest and lowest points correspond to the points of intersection of the minor axis and the rectangle.

    • 5

      Measure the distance from point "C" to point "A." Label this measurement as the distance "a," also know as length of the semi-major axis.

    • 6

      Measure the distance from the point "C" to point "B." Label this measurement as the distance "b," also know as length of the semi-minor axis.

    • 7

      Multiply the numerical value of "a" by itself, then multiply the value of "b" by itself. Add these two results together. Now take the square root of this result to obtain the distance between the focal point and the center of the ellipse, known as the "focal distance."

    • 8

      Measure to the right from point "C" on the major axis a distance equal to the "focal distance." Mark this point and label it "FR" as an abbreviation for the "right focal point."

    • 9

      Measure to the left from point "C" on the major axis a distance equal to the "focal distance." Mark this point and label it "FL" as an abbreviation for the "left focal point."

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